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Very recently, Lee et al.[10] have established generalization of the extended beta function, hypergeometric function and confluent hypergeometric function introduced by earlier researchers in this area. The aim of this research paper is to obtain some linear and bilinear generating relations for generalized extended Gauss, Appell and Lauricella hypergeometric functions in one, two and three variables by defining the further generalization of the extended fractional derivative operator. Some properties and Mellin transform of the generalized extended fractional derivative operator are also obtained.